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Conic Scalarizations for Approximate Efficient Solutions in Nonconvex Vector Optimization Problems

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Abstract

Nonlinear scalarization is a very important method to deal with the vector optimization problems. In this paper, some conic nonlinear scalarization characterizations of E-optimal points, weakly E-optimal points, and E-Benson properly efficient points proposed via improvement sets are established by a new scalarization function, respectively. These results improved and generalized some previously known results. As a special case, the scalarization of Benson properly efficient points is also given. Some examples are given to illustrate the main results.

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Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments that helped to improve the presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Chongqing Normal University, Chongqing, 401331, China

    Hui Guo

  2. College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China

    Wan-li Zhang

Authors
  1. Hui Guo
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  2. Wan-li Zhang
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Correspondence to Hui Guo.

Additional information

This research was supported by the National Natural Science Foundation of China (No. 11301574), Chongqing Municipal Education Commission (No. KJ1500310), and the Doctor Startup Fund of Chongqing Normal University (No.16XLB010).

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Guo, H., Zhang, Wl. Conic Scalarizations for Approximate Efficient Solutions in Nonconvex Vector Optimization Problems. J. Oper. Res. Soc. China 5, 419–430 (2017). https://doi.org/10.1007/s40305-016-0139-x

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  • DOI: https://doi.org/10.1007/s40305-016-0139-x

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